Solving literal equations

What is literal equation

What is the solving literal equation definition? It is when you have to solve a formula for a certain variable. Sometimes, you may need to solve for a variable that isn’t the standard one. An example of this is the distance formula. The formula to finding distance is:

D=rtD = rtD=rt

rrr stands for rate, and ttt stands for time. The standard variable that you’d solve for is DDD, for distance.

Perhaps in the question you’re faced with, you may need to find the rate rather than solving for distance. In that case, you may need to rearrange the formula so that you can solve the literal equation.

How to solve literal equations

Looking at literal equations, you may be worried about how you’ll go about solving them. However, they’re actually tackled in a way that’s very similar to how you’ve been solving equations all along. The only difference is that since you’re working with variables rather than numbers, you may not be able to simplify down your answer too much.

When you’re given a question that asks you to solve for a literal equation, you’ll be given a formula and then asked to solve for the indicated variable. That variable likely won’t be isolated onto its own side, which is what you’ll have to do. Take into account what you’ve done previously for equations where you’ve had to move terms to the other side of the equal sign. When you’ve got a positive number, take the negative of it from both sides. When you’ve got a number to multiply, take the division of it on both sides. When you’re done isolating the variable to equalling the rest of the variables moved over to the other side of the equal sign, you’ve successfully solved your literal equation!

Example problems

Question 1:

Solve each of the formulas for the indicated variable.

i) a=bca = bca=bc for ccc.

Solution:

We’ll have to isolate ccc, which means bbb has to be moved when we’re solving for a variable (ccc in this case).

ab=bcb\frac{a}{b} = \frac{bc}{b}​b​​a​​=​b​​bc​​

bbb on the right side cancels out each other, and we are left with:

ab=c\frac{a}{b} = c​b​​a​​=c

Our final answer:

c=abc = \frac{a}{b}c=​b​​a​​

ii) xy=z\frac{x}{y} = z​y​​x​​=z for xxx.

Solution:

xy=z\frac{x}{y} = z​y​​x​​=z

Multiply yyy to both sides in order to move yyy over to the right hand side.